Pith Number

pith:CK3KS4HI

pith:2016:CK3KS4HIB7VALGHU667R2R3ZG4

not attested not anchored not stored refs pending

The Optimal Pebbling Number of Staircase Graphs

Casey Tompkins, Ervin Gy\H{o}ri, Gyula Y. Katona, L\'aszl\'o F. Papp

arxiv:1611.09686 v1 · 2016-11-29 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CK3KS4HIB7VALGHU667R2R3ZG4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:56:13.288629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12b6a970e80fea0598f4f7bf1d4779372a861a6d3351fa57926d88b56ea4556e

Aliases

arxiv: 1611.09686 · arxiv_version: 1611.09686v1 · doi: 10.48550/arxiv.1611.09686 · pith_short_12: CK3KS4HIB7VA · pith_short_16: CK3KS4HIB7VALGHU · pith_short_8: CK3KS4HI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CK3KS4HIB7VALGHU667R2R3ZG4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 12b6a970e80fea0598f4f7bf1d4779372a861a6d3351fa57926d88b56ea4556e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a294cf164afc5afa7b1545dd889bc323540b6549be9745c5a80631625bd18f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-11-29T15:37:55Z",
    "title_canon_sha256": "893b0dc8b49ef09da9afe22d0ba39484ab13465076614c49f599e96869909814"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09686",
    "kind": "arxiv",
    "version": 1
  }
}